For example, I open an image and create a new view (View/New View menu).
Then when I use the rectangle selection tool, the solid line is visible
only in one view. The selection's non-solid line becomes visible in
both views.
Why the tool's solid line is not visible in both views?
Because tool displays are drawn onto the view, not the image.
Why the selection's non-solid line is visible in both views?
This is not necessarily true. The marching ants ('non-solid line') are only visible in views that have the 'Show selection' option enabled. The selection outline shows in all views of an image which are set to show it, because it is part of the image rather than the view.
Whether new views have 'show selection' enabled by default is controlled by an option in preferences. (Image windows->Appearance subsection)
Why the path or other objects would not be visible in both views?
? They are. Maybe you mean 'why should the path or other objects not be visible in both views' -- which is a question that someone else needs to answer.
I cannot answer your other questions.
What is your perfect solution?
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